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Smoothed Aggregation Multigrid for Cloth Simulation

Rasmus Tamstorf, Toby Jones, Stephen F. McCormick

SIGGRAPH AsiaIndustrial100 cites3 descendantsCFX

Algebraic multigrid method for accelerating cloth simulation on unstructured meshes with varying material properties and collision constraints.

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Abstract

Existing multigrid methods for cloth simulation are based on geometric multigrid. While good results have been reported, geometric methods are problematic for unstructured grids, widely varying material properties, and varying anisotropies, and they often have difficulty handling constraints arising from collisions. This paper applies the algebraic multigrid method known as smoothed aggregation to cloth simulation. This method is agnostic to the underlying tessellation, which can even vary over time, and it only requires the user to provide a fine-level mesh. To handle contact constraints efficiently, a prefiltered preconditioned conjugate gradient method is introduced. For highly efficient preconditioners, like the ones proposed here, prefiltering is essential, but, even for simple preconditioners, prefiltering provides significant benefits in the presence of many constraints. Numerical tests of the new approach on a range of examples confirm 6--8 x speedups on a fully dressed character with 371k vertices, and even larger speedups on synthetic examples.

How to read this

Category: Method: algebraic multigrid solver for cloth
Contributions: Applies smoothed-aggregation algebraic multigrid to cloth simulation, agnostic to tessellation (which may even vary over time) and requiring only a fine-level mesh.
Introduces a prefiltered preconditioned conjugate gradient method to handle contact constraints efficiently.
Reports 6 to 8x speedups on a fully dressed 371k-vertex character, with larger speedups on synthetic examples.
Context: Replaces geometric multigrid with algebraic multigrid for the implicit cloth solver in the lineage of Baraff and Witkin's Large Steps in Cloth Simulation.Builds on: Large Steps in Cloth Simulation
Correctness: Validated by numerical tests across a range of examples including a full garment; speedups assume the AMG plus prefiltered PCG setup suits the problem, and the prefiltering is reported as essential for efficient preconditioners under many constraints.
Clarity: Numerically dense; a first pass conveys why algebraic beats geometric multigrid here, with a careful second/third pass needed for the solver and prefiltering math.
How to read it: First pass for the motivation (unstructured meshes, varying materials, constraints); plan a thorough second pass on the AMG and prefiltered-PCG formulation if implementing the solver.

Builds on

Large Steps in Cloth Simulation 1998

Built upon by

Related work

CAMA: Contact-Aware Matrix Assembly with Unified Collision Handling for GPU-based Cloth Simulation 2016 / CGF
Continuum-based Strain Limiting 2009 / Eurographics
Projective Dynamics with Dry Frictional Contact 2020 / TOG
GPU-Based Simulation of Cloth Wrinkles at Submillimeter Levels 2021 / SIGGRAPH

Keywords

cloth simulation smoothed aggregation algebraic multigrid geometric multigrid preconditioned conjugate gradient prefiltered preconditioned cg thin shell simulation implicit time integration stiffness matrix collision handling strength of connection tentative interpolation operator galerkin coarse grid chebyshev smoother near-kernel components constraint null space baraff and witkin v-cycle

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